Clustering of Local Optima in Combinatorial Fitness Landscapes

  • Gabriela Ochoa
  • Sébastien Verel
  • Fabio Daolio
  • Marco Tomassini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6683)


Using the recently proposed model of combinatorial landscapes: local optima networks, we study the distribution of local optima in two classes of instances of the quadratic assignment problem. Our results indicate that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the optima networks possess a clear modular structure, while the networks belonging to the class of random uniform instances are less well partitionable into clusters. We briefly discuss the consequences of the findings for heuristically searching the corresponding problem spaces.


Local Optimum Spin Glass Community Detection Quadratic Assignment Problem Community Detection Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Tomassini, M., Vérel, S., Ochoa, G.: Complex-network analysis of combinatorial spaces: The NK landscape case. Phys. Rev. E 78(6), 066114 (2008)CrossRefGoogle Scholar
  2. 2.
    Vérel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Trans. on Evol. Comp. (2010) (to appear)Google Scholar
  3. 3.
    Doye, J.P.K.: The network topology of a potential energy landscape: a static scale-free network. Phys. Rev. Lett. 88, 238701 (2002)CrossRefGoogle Scholar
  4. 4.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Daolio, F., Vérel, S., Ochoa, G., Tomassini, M.: Local optima networks of the quadratic assignment problem. In: IEEE Congress on Evolutionary Computation, CEC 2010, pp. 3145–3152. IEEE Press, Los Alamitos (2010)Google Scholar
  6. 6.
    Knowles, J., Corne, D.: Instance generators and test suites for the multiobjective quadratic assignment problem. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 295–310. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Fortunato, S.: Community detection in graphs. Physics Reports 486, 75–174 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gabriela Ochoa
    • 1
  • Sébastien Verel
    • 2
  • Fabio Daolio
    • 3
  • Marco Tomassini
    • 3
  1. 1.School of Computer ScienceUniversity of NottinghamNottinghamUK
  2. 2.INRIA Lille - Nord Europe and University of Nice Sophia-AntipolisFrance
  3. 3.Information Systems DepartmentUniversity of LausanneLausanneSwitzerland

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